Koeman was confirmed as the Everton manager on Tuesday after signing a three-year contract worth £6m a year to succeed Roberto Martínez at Goodison Park. Farhad Moshiri, Everton’s major shareholder, last week agreed a £5m compensation package with Southampton to secure the 53-year-old’s exit from St Mary’s Stadium.

The former Ajax, PSV Eindhoven, Valencia and Benfica coach was lured north by a lucrative contract but also the promise of the biggest transfer budget in Everton’s history. Among the big name targets under consideration is Witsel, who is looking to leave Zenit St Petersburg after the European Championship. The 27-year-old, who played in central midfield for Belgium in their 2-0 defeat by Italy on Monday, has spent four years in Russia and is keen on a move to the Premier League.

Zenit want to recoup a sizeable part of the €40m fee they paid to activate Witsel’s buyout clause at Benfica in 2012. The former Standard Liège player has 12 months remaining on his contract with the Russian club and it will be left to Koeman to decide whether to pursue a deal for the international colleague of Everton players Romelu Lukaku and Kevin Mirallas.

Tim Krul, the Newcastle United goalkeeper, is another player on Everton’s radar, with the Holland international having only 12 months remaining on his contract. Krul is seen as a first-choice goalkeeper at Everton following Tim Howard’s departure. Everton have also been linked with the West Bromwich Albion forward Saido Berahino, with Lukaku expected to depart this summer.

Koeman will be joined at Goodison by his brother Erwin and compatriot Jan Kluitenberg, the assistant manager and the coach at Southampton respectively. The man who scored the winner for Barcelona in the 1992 European Cup final had 12 months remaining on his contract at St Mary’s and indicated he would sign an extension until Everton turned his head with their contract offer and the size of their ambition. Moshiri made Koeman his first choice having decided to end Martínez’s three-year reign before the end of last season and is also looking at two sites for a new stadium for Everton.

“It’s a great feeling,” said Koeman, who has been in the Caribbean on a family holiday. “It was amazing when I had the first contact with the chairman [Bill Kenwright] and Farhad Moshiri about their interest. I was interested to listen and to hear about their big project, their vision which they want over the coming seasons. I am pleased to be part of that - it’s really enjoyable.

“Everton have a big history and we will do everything we can to try to reach what was reached in the past. That is difficult but I believe with all of the people involved at Everton and with the fans that anything is possible. The ambition is always to give the fans spirit so they can see the team is fighting for everything and we want to try to play good football. They are the basics for what you need to get good results. Being a footballer these days isn’t like being a player 20 or 30 years ago because it’s a really tough job and you have to be disciplined and live for it.”

Everton also considered Frank de Boer, Manuel Pellegrini and Unai Emery as replacements for Martínez but Koeman was always the preferred choice. Kenwright said: “We are really pleased to have secured the man who was our No1 target from the moment we set out to appoint a new manager. Ronald has such a strong track record in the game, instantly commanding respect for what he achieved as a player and for his qualities and accomplishments as a manager.”

Southampton issued a statement following Koeman’s exit that read: “The search has already begun for the right appointment who can take the club to the next level and build on our track record of recent success, which culminated in a sixth-place finish in last season’s Premier League, as well as qualification for the group stages of the Europa League.”